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Research Papers

Optimization of the Loaded Contact Pattern in Hypoid Gears by Automatic Topography Modification

[+] Author and Article Information
Alessio Artoni1

Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione, University of Pisa, Via Diotisalvi 2, 56122 Pisa, Italyalessio.artoni@ing.unipi.it

Andrea Bracci

Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione, University of Pisa, Via Diotisalvi 2, 56122 Pisa, Italyandrea.bracci@ing.unipi.it

Marco Gabiccini

Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione, University of Pisa, Via Diotisalvi 2, 56122 Pisa, Italym.gabiccini@ing.unipi.it

Massimo Guiggiani

Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione, University of Pisa, Via Diotisalvi 2, 56122 Pisa, Italym.guiggiani@ing.unipi.it

Fig. 5: spiral bevel gear drive, Z29-Z53, torque on pinion: 417Nm.

2.5 GHz processor, 1 Gbyte RAM.

The contact patterns calculated by HFM are slight heel patterns. If strict design prescriptions required superior optimality, the whole calculation could be repeated after slightly offsetting the target quadrilaterals toward the toe.

1

Corresponding author.

J. Mech. Des 131(1), 011008 (Dec 15, 2008) (9 pages) doi:10.1115/1.3013844 History: Received July 17, 2008; Revised September 22, 2008; Published December 15, 2008

Systematic optimization of the tooth contact pattern under load is an open problem in the design of spiral bevel and hypoid gears. In order to enhance its shape and position, gear engineers have been assisted by numerical tools based on trial-and-error approaches, and/or they have been relying on the expertise of skilled operators. The present paper proposes a fully automatic procedure to optimize the loaded tooth contact pattern, with the advantage of eventually reducing design time and cost. The main problem was split into two identification subproblems: first, to identify the ease-off topography capable of optimizing the contact pattern; second, to identify the machine-tool setting variations required to obtain such ease-off modifications. Both of them were formulated and solved as unconstrained nonlinear optimization problems. In addition, an original strategy to quickly approximate the tooth contact pattern under load was conceived. The results obtained were very satisfactory in terms of accuracy, robustness, and computational speed. They also suggest that the time required to optimize the contact pattern can be significantly reduced compared with typical time frames. A sound mathematical framework ensures results independent of the practitioner’s subjective decision-making process. By defining a proper objective function, the proposed method can also be applied to affect other contact properties, such as to improve the motion graph or to decrease the sensitivity of the transmission to assembly errors. Furthermore, it can be easily adapted to any gear drive by virtue of its systematic and versatile nature.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Outside blade of the grinding wheel (conjugate to the tooth concave side)

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Figure 2

Schematic arrangement of the cradle-style machine

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Figure 3

Approximation of the instantaneous contact area

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Figure 4

Intersection curve approximating an instantaneous contact area (pinion tooth); (a) u1v1-plane, (b) r1z1-plane

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Figure 5

HFM contact pattern versus convex hull approximations for different values of c

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Figure 6

Target contact pattern under load according to Ref. 25, Annex F

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Figure 7

Current and target contact patterns: some definitions

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Figure 8

Definition of the to-be-minimized residual ease-off

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Figure 9

Basic loaded tooth contact patterns (gray-shaded areas: HFM contact patterns; black solid curves: SLTCA convex hull polygons)

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Figure 10

Target and basic contact patterns; (a) pinion tooth, (b) gear tooth

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Figure 11

Optimal ease-off topography, automatically identified (maximum-to-minimum value: 250 μm)

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Figure 12

Optimized loaded tooth contact patterns (gray-shaded areas: HFM contact patterns; black solid curves: SLTCA convex hull polygons; dashed quadrilaterals: target contact patterns)

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Figure 13

Standard set: residual ease-off values

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Figure 14

Standard set: HFM contact pattern on the pinion tooth; (a) imposing the optimal ease-off topography, (b) with optimal values of the standard set parameters

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Figure 15

Kinematic set: residual ease-off values

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Figure 16

Kinematic set: HFM contact pattern on the pinion tooth; (a) imposing the optimal ease-off topography, (b) with optimal values of the kinetic set parameters

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